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Author Topic: 3D Knots  (Read 8143 times)

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Offline Ashish

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3D Knots
« on: March 09, 2018, 05:57:55 am »
Some mathematical knots or geometry....
http://paulbourke.net/geometry/knots/
Code: QB64: [Select]
  1. 'Coded in QB64 by Ashish on 9 March, 2018
  2. 'http://paulbourke.net/geometry/knots/
  3. _TITLE "3D Knot [Press space for next knot]"
  4.  
  5. SCREEN _NEWIMAGE(700, 700, 32)
  6.  
  7. TYPE vec3
  8.     x AS SINGLE
  9.     y AS SINGLE
  10.     z AS SINGLE
  13.     SUB gluLookAt (BYVAL eyeX#, BYVAL eyeY#, BYVAL eyeZ#, BYVAL centerX#, BYVAL centerY#, BYVAL centerZ#, BYVAL upX#, BYVAL upY#, BYVAL upZ#)
  15.  
  16. DIM SHARED glAllow AS _BYTE, knot_type, ma
  17. knot_type = 1
  18. glAllow = -1
  19.  
  21.     k& = _KEYHIT
  22.     IF k& = ASC(" ") THEN
  23.         knot_type = knot_type + 1
  24.         ma = 0
  25.         IF knot_type > 7 THEN knot_type = 1
  26.     END IF
  27.     _LIMIT 60
  29.  
  30. SUB _GL ()
  31.     STATIC glInit, clock
  32.     ' static r, pos, theta, phi, beta
  33.  
  34.     IF NOT glAllow THEN EXIT SUB
  35.  
  36.     IF NOT glInit THEN
  37.         glInit = -1
  38.         aspect# = _WIDTH / _HEIGHT
  39.         _glViewport 0, 0, _WIDTH, _HEIGHT
  40.     END IF
  41.    
  42.     _glEnable _GL_DEPTH_TEST
  43.     _glDepthMask _GL_TRUE
  44.    
  45.     _glMatrixMode _GL_PROJECTION
  47.     _gluPerspective 45.0, aspect#, 1.0, 100.0
  48.    
  49.     _glMatrixMode _GL_MODELVIEW
  51.     ' gluLookAt 0,0,-1,0,0,0,0,1,0
  52.    
  53.     _glColor3f 1, 1, 1
  54.     _glTranslatef 0, 0, 0
  55.     _glRotatef clock * 90, 0, 1, 0
  56.     _glLineWidth 3.0
  57.    
  58.     SELECT CASE knot_type
  59.         CASE 7
  60.             _glBegin _GL_LINE_STRIP
  61.             FOR beta = 0 TO ma STEP .005
  62.                 r = .3 + .6 * SIN(6 * beta)
  63.                 theta = 2 * beta
  64.                 phi = _PI(.6) * SIN(12 * beta)
  65.                 x = r * COS(phi) * COS(theta)
  66.                 y = r * COS(phi) * SIN(theta)
  67.                 z = r * SIN(phi)
  68.                 _glColor3f map(x, -1, 1, 0, 1), map(y, -1, 1, 0, 1), map(z, -1, 1, 0, 1)
  69.                 _glVertex3f x, y, z
  70.             NEXT
  71.             _glEnd
  72.             IF ma <= _PI THEN ma = ma + .005
  73.         CASE 6
  74.             _glBegin _GL_LINE_STRIP
  75.             FOR beta = 0 TO ma STEP .005
  76.                 r = 1.2 * 0.6 * SIN(_PI(.5) * 6 * beta)
  77.                 theta = 4 * beta
  78.                 phi = _PI(.2) * SIN(6 * beta)
  79.                 x = r * COS(phi) * COS(theta)
  80.                 y = r * COS(phi) * SIN(theta)
  81.                 z = r * SIN(phi)
  82.                 _glColor3f map(x, -1, 1, 0, 1), map(y, -1, 1, 0, 1), map(z, -1, 1, 0, 1)
  83.                 _glVertex3f x, y, z
  84.             NEXT
  85.             _glEnd
  86.             IF ma <= _PI(2) THEN ma = ma + .005
  87.         CASE 5
  88.             k = 1
  89.             _glBegin _GL_LINE_STRIP
  90.             FOR u = 0 TO ma STEP .005
  91.                 x = COS(u) * (2 - COS(2 * u / (2 * k + 1))) / 5
  92.                 y = SIN(u) * (2 - COS(2 * u / (2 * k + 1))) / 5
  93.                 z = -SIN(2 * u / (2 * k + 1)) / 5
  94.                 _glColor3f map(x, -1, 1, 0, 1), map(y, -1, 1, 0, 1), map(z, -1, 1, 0, 1)
  95.                 _glVertex3f x, y, z
  96.             NEXT
  97.             _glEnd
  98.             IF ma < _PI(4 * k + 2) THEN ma = ma + .045
  99.         CASE 4
  100.             k = 2
  101.             _glBegin _GL_LINE_STRIP
  102.             FOR u = 0 TO ma STEP .005
  103.                 x = COS(u) * (2 - COS(2 * u / (2 * k + 1))) / 5
  104.                 y = SIN(u) * (2 - COS(2 * u / (2 * k + 1))) / 5
  105.                 z = -SIN(2 * u / (2 * k + 1)) / 5
  106.                 _glColor3f map(x, -1, 1, 0, 1), map(y, -1, 1, 0, 1), map(z, -1, 1, 0, 1)
  107.                 _glVertex3f x, y, z
  108.             NEXT
  109.             _glEnd
  110.             IF ma < _PI(4 * k + 2) THEN ma = ma + .045
  111.         CASE 3
  112.             k = 3
  113.             _glBegin _GL_LINE_STRIP
  114.             FOR u = 0 TO ma STEP .005
  115.                 x = COS(u) * (2 - COS(2 * u / (2 * k + 1))) / 5
  116.                 y = SIN(u) * (2 - COS(2 * u / (2 * k + 1))) / 5
  117.                 z = -SIN(2 * u / (2 * k + 1)) / 5
  118.                 _glColor3f map(x, -1, 1, 0, 1), map(y, -1, 1, 0, 1), map(z, -1, 1, 0, 1)
  119.                 _glVertex3f x, y, z
  120.             NEXT
  121.             _glEnd
  122.             IF ma < _PI(4 * k + 2) THEN ma = ma + .045
  123.         CASE 2
  124.             _glBegin _GL_LINE_STRIP
  125.             FOR u = 0 TO ma STEP .005
  126.                 x = (41 * COS(u) - 18 * SIN(u) - 83 * COS(2 * u) - 83 * SIN(2 * u) - 11 * COS(3 * u) + 27 * SIN(3 * u)) / 200
  127.                 y = (36 * COS(u) + 27 * SIN(u) - 113 * COS(2 * u) + 30 * SIN(2 * u) + 11 * COS(3 * u) - 27 * SIN(3 * u)) / 200
  128.                 z = (45 * SIN(u) - 30 * COS(2 * u) + 113 * SIN(2 * u) - 11 * COS(3 * u) + 27 * SIN(3 * u)) / 200
  129.                 _glColor3f map(x, -1, 1, 0, 1), map(y, -1, 1, 0, 1), map(z, -1, 1, 0, 1)
  130.                 _glVertex3f x, y, z
  131.             NEXT
  132.             _glEnd
  133.             IF ma < _PI(2) THEN ma = ma + .005
  134.         CASE 1
  135.             _glBegin _GL_LINE_STRIP
  136.             FOR u = 0 TO ma STEP .005
  137.                 x = (-22 * COS(u) - 128 * SIN(u) - 44 * COS(3 * u) - 78 * SIN(3 * u)) / 200
  138.                 y = (-10 * COS(2 * u) - 27 * SIN(2 * u) + 38 * COS(4 * u) + 46 * SIN(4 * u)) / 200
  139.                 z = (70 * COS(3 * u) - 40 * SIN(3 * u)) / 200
  140.                 _glColor3f map(x, -1, 1, 0, 1), map(y, -1, 1, 0, 1), map(z, -1, 1, 0, 1)
  141.                 _glVertex3f x, y, z
  142.             NEXT
  143.             _glEnd
  144.             IF ma < _PI(2) THEN ma = ma + .005
  145.     END SELECT
  146.     _glFlush
  147.    
  148.     clock = clock + .01
  150.  
  151. FUNCTION map! (value!, minRange!, maxRange!, newMinRange!, newMaxRange!)
  152.     map! = ((value! - minRange!) / (maxRange! - minRange!)) * (newMaxRange! - newMinRange!) + newMinRange!
  154.  
  155.  
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Offline bplus

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Re: 3D Knots
« Reply #1 on: March 09, 2018, 07:25:28 am »
WoW! very nice!

Bravo!
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Offline Ashish

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Re: 3D Knots
« Reply #2 on: March 09, 2018, 07:58:25 am »
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Offline Pete

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Re: 3D Knots
« Reply #3 on: March 09, 2018, 11:32:39 am »
Knot quite what I expected, but it did tie up my computer for awhile.

Funny how our minds work. It creates an optical illusion of the line going under itself. If you concentrate on a 2-D level, you can change that image, but you really have to stay focused. Neat.

Pete :D
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Offline Ashish

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Re: 3D Knots
« Reply #4 on: March 10, 2018, 01:23:24 am »
Quote from: Pete on March 09, 2018, 11:32:39 am
Knot quite what I expected, but it did tie up my computer for awhile.

Funny how our minds work. It creates an optical illusion of the line going under itself. If you concentrate on a 2-D level, you can change that image, but you really have to stay focused. Neat.

Pete :D
Thanks Pete! I appreciate your thought.
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FellippeHeitor

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Re: 3D Knots
« Reply #5 on: March 18, 2018, 08:38:21 pm »
SUB _GL is treated differently by QB64. You don't call it, but it is run at ~60fps (or whatever the refresh rate on your system is).
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Offline Ashish

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Re: 3D Knots
« Reply #6 on: March 19, 2018, 03:09:36 am »
Quote from: [banned user] on March 18, 2018, 04:29:26 pm
Quite impressive, but can you please explain to me how it is working when there is no call to the _GL subroutine?

As Fellippe said, SUB _GL is special subroutine which when detected by QB64, allows you to use OpenGL commands in it.
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